Enhanced superconductivity in FeSe/SrTiO₃ from the combination of forward scattering phonons and spin fluctuations

We study the effect of combining spin fluctuations and forward scattering electron-phonon (e-ph) coupling on the superconductivity in the FeSe/SrTiO3 system modeled by a phenomenological two-band Hubbard model with long-range {e-ph} interactions. We treat the electron and phonon degrees of freedom on an equal footing using a fully self-consistent FLEX plus Migdal-Eliashberg calculation, which includes a self-consistent determination of the spin fluctuation spectrum. Based on FeSe monolayers, we focus on the case where one of the bands lies below the Fermi level (i.e. incipient), and demonstrate that the combined interactions can enhance or suppress Tc, depending on their relative strength. For a suitable choice of parameters, the spin-fluctuation mechanism yields a Tc ≈46.8 K incipient s± superconductor, consistent with surface-doped FeSe thin films. A forward-focused e-ph interaction further enhances the Tc, as observed in monolayer FeSe on SrTiO3